Presented are 44 examples in which students are invited to guess what pattern of numbers is emerging and to decide whether the pattern will persist. Topics of examples include Pascal's triangle, integers, vertices, Fibonacci numbers, power series, partition functions, and Euler's theorem. The answers to all problems are included. (KR)

Artificial intelligence (AI) is the field of scientific inquiry concerned with designing machine systems that can simulate human mental processes. The field draws upon theoretical constructs from a wide variety of disciplines, including mathematics, psychology, linguistics, neurophysiology, computer science, and electronic engineering. Some of the…

An overview of a variety of interesting teaching techniques is given to assist school personnel in strengthening their overall mathematics programs in the first eight grades. The problem-solving approaches recommended are so designed that they should be useful in every subject. The materials could also be used as a basis for teacher in-service…

The brain works by making patterns, and this process can be visualized through a medium called visual tools. The book discusses three types of visual tools: brainstorming webs, task-specific organizers, and thinking-process maps. Sample lessons, assessments, and descriptions of visual tools in action are included. Emphasis is placed on the…

Acknowledging a growing national awareness of the need for direct instruction in higher order thinking skills within public education, this paper describes an instructional model for reinforcing thinking skills in the classroom, kindergarten through grade 12. Following an introduction justifying the model's reliance on the processing of…

This paper reviews some recent research on the component skills necessary to learn to read by phonic techniques. The review is divided into four sections, each relating research on one of the skills necessary for novel word decoding. The four skill areas are: (1) learning invariant grapheme-phoneme correspondences; (2) relating the isolated letter…

A computer program is presented for the billiard ball problem. It can be integrated into a lesson on inductive reasoning and suggests several ways to do so. (MNS)

A useful approach for developing insights and discovering patterns is to examine numbers in relation to the number of their divisors. A teaching procedure for this approach is presented, with questions, answers, and homework suggestions. (MNS)

Describes a card trick that provides opportunities for students to discover patterns, work with variables, create tables, and ponder mathematics. Students at various levels of ability are able to enjoy the trick, and mathematical discourse is promoted within the classroom. (AIM)

Described are some ways in which individual states code driver's license numbers. The encoding of month, date of birth, year of birth, sex, and others involving elementary mathematics and the use of an elaborate system of hashing functions in describing the first, middle, and last names are discussed. (KR)

Pattern work is now undertaken as early as kindergarten, and both researchers and teachers have discovered that children engage in pattern work with great enthusiasm and innate ability. Having some flexibility in pattern perception and selecting mathematically useful patterns require some training, although there is nothing particularly algebraic…

This study addresses the question: "To what extent are teacher assigned subject specific grades useful for data driven decision making in schools?" Recently, schools have been urged to bring teachers and school leaders together around student-level data in an effort to increase dialogue, collaboration and professional communities to…

In order to teach in the content area, a teacher must accept five basic premises: (1) Reading in the content field is part of the total school program. (2) All teachers are responsible for helping students read the text in a specific subject. (3) The focus of teaching is changed from merely teaching content to how to read and understand the…

An investigation of patterns in magic triangles leads to a number of discoveries concerning the sums of sides and corners. (MP)

A series of activities involving figurate numbers that allow students at various levels to integrate numerical, geometric, arithmetic, patterning, measuring, and problem-solving skills are presented. A discussion of the geometric and numerical aspects of figurate numbers is included. Appended are IBM Logo procedures that will create pentagonal…